Consider the following linear programming (LP) constraints: x1 + x2 0 1. Sketch the feasible region, and identify all extreme points (vertices). 2. Transform the above system of inequalities to a system of equalities, by adding slack or surplus variables. 3. Consider the matrix form of the above LP feasible region such as Ax0, determine the entries and dimensions of Matrix A, and vector b? 4. If 2 columns of matrix A are chosen to form a square submatrix, how many submatrices are possible? Identify them. 5. Let us enumerate all choices of m= 2 out of n = 4 columns of A, that lead to a basis. Show all possible bases, basic solutions, and then classify each basic solution, whether it is feasible or non-feasible. Use the table below: Remarks (why?) Solution (x1,x2,s1,s2) Is it a basic feasible solution? A-submatrix Can it be a BASIS? [A1, A2] [A1, A4] [A2, A3] [A2, A4) [A3, A4) [A1, A3]